Boundaries for algebras of holomorphic functions

Let Au(BG) be the Banach algebra of all complex valued functions defined on the closed unit ball BG of a complex Banach space G which are uniformly continuous on BG and holomorphic in the interior of BG, endowed with the sup norm. A characterization of the boundaries for Au(BG) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129–151. The non-existence of the Shilov boundary for Au(BG) is also proved.  2003 Elsevier Science (USA). All rights reserved.